Juice the lemon and pour the juice into a small nonreactive bowl. (Save the lemon halves.) Put the seeds in a piece of cheesecloth along with the peppercorns, allspice berries, and bay leaves, and give it a few whacks with a hammer or rolling pin. Add the bag to the lemon juice.
Cut the strawberries into quarters, or if they are small, you can cut them in half. If you have a mix, cut them all so they are approximately the same size. You just don’t want them too small.
Toss the strawberries in a separate bowl with the sugar, vinegar, and salt. Cover and let sit at room temperature for a few hours (2-3), stirring occasionally.
Set a colander or large strainer over a wide, nonreactive cooking pot. Scrape the berries and their juices into the colander or strainer so the juices go into the cooking pot. Remove the colander with the macerated berries in it and set it aside. (I put it back in the bowl so it doesn’t drip on the counter.)
Add the lemon juice, the spice bag, the reserved lemon halves, and the butter to the strawberry juices in the pot and cook over medium-high heat until the juices begin to thicken, about 6 or 7 minutes. Add the strawberries and continue to cook, stirring gently every so often, until the berries are plump and softened, but not bursting apart. It will take about 8 to 10 minutes. You want the berries to remain in fairly distinct pieces.
Remove from heat, then discard the spice bag as well as the lemon rinds. Grind a bit more black pepper into the strawberries and ladle them into jars and cover.
Storage: The pickled strawberries can be kept in the refrigerator for up to 1 month. If you wish to can them, check the guidelines and directions at the USDA website.